(4h+8)(2h-3)=0

Solution for (4h+8)(2h-3)=0 equation:

Simplifying
(4h + 8)(2h + -3) = 0

Reorder the terms:
(8 + 4h)(2h + -3) = 0

Reorder the terms:
(8 + 4h)(-3 + 2h) = 0

Multiply (8 + 4h) * (-3 + 2h)
(8(-3 + 2h) + 4h * (-3 + 2h)) = 0
((-3 * 8 + 2h * 8) + 4h * (-3 + 2h)) = 0
((-24 + 16h) + 4h * (-3 + 2h)) = 0
(-24 + 16h + (-3 * 4h + 2h * 4h)) = 0
(-24 + 16h + (-12h + 8h2)) = 0

Combine like terms: 16h + -12h = 4h
(-24 + 4h + 8h2) = 0

Solving
-24 + 4h + 8h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + h + 2h2) = 0

Factor a trinomial.
4((-2 + -1h)(3 + -2h)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -1h)' equal to zero and attempt to solve:

Simplifying
-2 + -1h = 0

Solving
-2 + -1h = 0

Move all terms containing h to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1h = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1h = 0 + 2
-1h = 0 + 2

Combine like terms: 0 + 2 = 2
-1h = 2

Divide each side by '-1'.
h = -2

Simplifying
h = -2
Subproblem 2
Set the factor '(3 + -2h)' equal to zero and attempt to solve:

Simplifying
3 + -2h = 0

Solving
3 + -2h = 0

Move all terms containing h to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2h = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2h = 0 + -3
-2h = 0 + -3

Combine like terms: 0 + -3 = -3
-2h = -3

Divide each side by '-2'.
h = 1.5

Simplifying
h = 1.5
Solution
h = {-2, 1.5}